The Factoring Process

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The Factoring Process
Algebra II

• Presented by Mr. R. A. Moore
• St. Albans High School
• July 2, 1999

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Greatest Common Factor

• Look for the greatest common factor

3x³ - 12x² 6x
(3x)x² - (3x)4x (3x)2
(3x)(x² - 4x 2)
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Is The Remaining Polynomial a Binomial? (2
terms)

• If noClick Here
• If yes
• Is it a difference of two squares?
• Yes
• No

Example x² - y²
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Binomial

• Is it a difference of two cubes?
• Yes
• No

Example x³ - y³
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Difference of Two Cubes
Example

• Click Here

x³ - y³ (x - y)(x² xy y²)
The difference of two cubes equals the product of
a binomial factor times a trinomial factor. The
binomial factor is the difference of the two
numbers being cubed. The trinomial factor is
formed by squaring the first term of the binomial
factor, add the product of the two binomial
terms, and add the square of the second binomial
term.
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Binomial

• Is it the sum of two cubes?
• Yes
• No

Example x³ y³
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Sum of Two Cubes
Example

• Click Here

x³ y³ (x y)(x² - xy y²)
The sum of two cubes equals the product of a
binomial factor times a trinomial factor. The
binomial factor is the sum of the two numbers
being cubed. The trinomial factor is formed by
squaring the first term of the binomial factor,
subtract the product of the two binomial terms,
and add the square of the second binomial term.
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Prime Binomial

• The binomial is prime and cannot be factored
• Click Here

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9
Is the Remaining Polynomial a Trinomial? (3
terms)

• If noClick Here
• If yes
• Is it a trinomial square (the square of a
  binomial)?
• Yes
• No

Example x² - 2xy y²
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Trinomial

• Is the lead coefficient 1?
• Yes
• No

Example x² - 5x 6
1
There is no number in front of the x² so the lead
coefficient is 1.
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Trinomial

• The lead coefficient is something other than 1
• Use the appropriate table to find a sum for the
  middle term and factor by grouping terms

Example 3x² 10x - 8
Click Here
12
Trinomial

• The lead coefficient is something other than 1

Example 3x² 10x - 8
3 X -8
3x² - 2x 12x - 8
-24
10
-1,24 23
x(3x - 2) 4(3x - 2)
-2,12 10
(3x - 2)
(x
4)
Click Here
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The Lead Coefficient is 1
Factor using the appropriate table.
x² - 5x 6
(x )(x )
- 2
- 3
6
-5
-1,-6 -7
-2,-3 -5
Click Here
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More Than Three Terms

• If there are more than three terms, you will have
  to factor by grouping.
• If there are four terms, group by
• putting two terms in each group or
• three terms in one group and one term in the
  other
• Click Here

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Did It Work?

• If none of these methods worked, the polynomial
  is probably prime
• Click Here

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Factor It (More Than 3 Terms)

• More than three terms

(grouping two terms and two terms)
x(a b)
ax bx - ay - by
- y(a b)
(x - y)(a b)
Click Here
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Factor It

• Factor the polynomial accordingly

x² - y² (x y)(x - y)
Click Here
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Factor It (More Than 3 Terms)

• More than three terms
• (group three terms and one term)

x² 2xy y² - 25
(x² 2xy y²) - 25

(x y)² - 25
(x y 5)(x y - 5)
Click Here
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Bibliography

• Foster, Alan G., Joan M. Gell, Berchie W. Gordon,
  James N. Rath, and Leslie J. Winters, Merrill
  Algebra 2 With Trigonometry. Columbus, Ohio
  Macmillan/McGraw-Hill Publishing Company,1992
• Clip Art Credit Clip-Art.com
• Sound Clip Credit Bugs Bunny Sound Clips

www.magpage.com/msmsmith/wave/looneytunes/bugs/mai
n.html
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Factor the trinomial
x² 2xy y²
(x y)²
Click Here
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WVDE IGOS

• A2.3 continue to factor polynomials by
  applying various methods of
  factoring including the sum and difference of
  cubes
• A2.20 use appropriate software to practice and
  master Algebra II objectives